Most of it's already been said, but I'll add my 2 Cents.
AI: I have an AXMC with 3 calibres (308, 300 WM and 338LM). As everyone has said already, extremely smooth bolt, easy calibre changes plus it's easy to get other barrels. 10 round AIAW mags for 308 and the mag cutout on the left side is nice. The negatives... It's expensive. Mine are all AI, including the AI Tactical muzzle brakes for each of the three barrels. You can buy new barrels along with another brand of muzzle brake. So you can bring the costs down if not going all AI parts. The one disadvantage to the AXMC is the plastic pistol grip. AI was slower than the rest to modify their chassis system. It fits me and I don't mind it. But you have the seem and it's a throw back from AI of older. If an AI collector, though the AXMC might be the one to get. Especially if you can get a good deal on one.
The AXSR. If buying new I would definitely get one. It fixes the pistol grip issue of being a plastic throwback and goes with an Ergo grip. The AI chassis system seemed to be gradually going toward a more Cadex like design. The AXSR fixes this one negative of the AXMC. However it's not all perfect. You lose the much loved AI AW style 3 position safety and the AXSR is the American product. The European one with the metric threads etc, is the MK3 not the AXSR. So no distinct AI tactical muzzle brake. With the AXSR it uses the American threads and therefore an excellent Insite Arms Heathen muzzle brake. Not a deal breaker for me and it's the most up to date version out there. Barrels are interchangeable with the AXMC but not the bolts. I doubt anyone would be disappointed with this rifle. The only real negative is price.
Another favourite of mine is the Desert Tech. I own two Desert Tech SRS A1 rifles and a SRS A2. There is also the M2 which is the newest long range version with a 30 moa top rail and Arca on the bottom. They are bullpups, mags are mediocre and not super smooth, although you don't notice when you're in position and cycling the rifle. They use Walther Lothar barrels, much like a lot of the AI rifles and you can get aftermarket barrels for them. The Calibre changes are fast and as good or better than the AI. If thinking PRS or other specific shooting sports, then it's likely not the rifle for you. But as a precision tactical rifle, its' very accurate and a high end contender. I'm a fan. Plus deals can often be found that make them one of the more affordable options. Especially since bolts/barrels are interchangeable among all the SRA A1, A2 and M2 rifles.
The SRS A1. This would be my choice for a less expensive long range setup. Top rail which I mount an over bore bipod on. Trigger is excellent and highly adjustable (not as nice as the the AI though). It's the older and heavier option, which doesn't really matter if you're shooting long rang 338LM. Plus they do include the monopod if you're using the glass for an extended period of time. Not a big deal to me, but it is an expensive option if you want it in the A2 (Which you don't).
The SRS A2. This is the only one of the bunch listed that I wouldn't have an issue shooting off hand. It's fairly light compared to the others, all of which are boat anchors. The handguard is Mlok and interchangeable for the shorter covert version. If thinking big bore shooting and longer barrels/range etc, then the M2 is the newest and the best option for that.
The Barrett MRAD. I looked at these, I really looked at these. The reason I didn't go this route were the different Gens, requiring a conversion piece if you have an older gen along with the lack of calibre conversion kits. Most of the MRAD rifles I saw for sale, came with one calibre. But looking around, I couldn't find kits to add to it. There's not much point in having a multi calibre rifle with only one Calibre. Also I like the looks of the Gen 2 with the Mlok rail. Reminded me of my LMT MRP rifles. However, there were reported incidents with a batch of mil contract mk22 which also included some of the rifles bought in the Civilian market with the handguard/upper receiver cracking. Knowing my luck, I'd end up with one. Considering I couldn't even find conversion kits, I had little to no faith in any support from Barrett. If you can find a good one with multiple calibres, then this rifle would likely make you happy and is a contender with all the others mentioned. Cool rifles, although looks a little too much like a bolt action AR10 to me. But.. had I found one that was perfect, I would have likely bought it.
The Cadex Kraken. I don't own one, yet. Deal pending. I do however have a Cadex Guardian and had a Cadex Tremor 50BMG along with a number of their Chassis. I am a fan. I like their chassis and the rifles are built well. Not as smooth as an AI, however they smooth out with use and when properly oiled. I consider these to be high end rifles and like the other options listed, they are build like tanks. The trigger, I like it but others will likely favour the AI or possible a trigger tech. I have no concerns with the trigger. It's decent, but the AI is easier. Calibre changes.. Mareshow has a good video out there showing it. Not as quick as the others mentioned. But there are advantages. Return to zero for once. I will note that I have never heard any AI AW or AI AE owners complaining about the calibre or barrel changes (yes you can change the barrels out on those with a special barrel wrench and barrel vise) and the Kraken looks to be better than that. The bar near the scope looks a bit disconcerting, however I haven't heard of any instances with issues. The barrels are Bartlein and specific to the rifle. As mentioned you would have to order from Cadex or buy a set.
Mags. Advantage or disadvantage? The Cadex Kraken uses AICS pattern mags. With my AE MKIII one of the negatives was that it didn't use the AW mag which is dual stack and sits lower. But is it really a negative? I have a lot of the AICS mags, including a number of 12 rounders. You can get these mags from a number of different sources and they are the most popular system out there. They are high quality, affordable and almost universal. While the others are proprietary, often hard to get and expensive. I actually consider this a potential advantage with the Kraken.
One of the biggest issues with the Cadex Kraken is frankly how poorly the retailers sell/market them. Only one company seemed to sell full deployment kits. The rest will sell the rifle only. WTF is with that? You need the Cadex tools to change the calibres which you need to buy and most don't even offer that for sale. Again you don't want only one calibre with a multi calibre system. I know Cadex is busy with rifles for Ukraine, but the roll out of the Kraken hasn't really lived up to expectations. This is a rifle that is significantly less expensive for Canadians than an AI or Barrett etc. It's a solid high end rifle that offers ergonomics that AI has just now caught up with (Chassis design). Rant over.
Sako TRG M10. Over priced. I love my older TRG22 rifles, but the newest one is really over priced. Even the accessories for the TRG22 are ridiculous. The TRG22 bipod for example.. Luckily I found one second hand. Brand new it's robbery. Mags as well. I have no doubt it's an excellent rifle, but you'll be paying for it and I don't consider it better than an AI. If it's a choice between the AI and Sako, I'll take the AI any day. Unless it's a smoking deal like I had with my TRG22 rifles, I would look elsewhere. That's also the problem I have with the Steyr M1. You're at AI pricing. Just get the AI.
One suggestion. If you note Bartok5 has a pelican style case with the various barrels/bolts etc. This is what you want. I prefer soft cases for going to the range, but if you have all the calibre changes/bolts/mags etc it gets very heavy and is poorly organized in a soft case. The reality is you're not likely to change calibres at the range and it's better to have everything in an organized kit. I'll be doing this for my Multi calibre rifles going forward. Realized this after getting my AI AXMC. If I want two calibres, then I'll grab two for the soft case. It's just easier storage and organization to have a solid case with everything and then to pick from that.
Bottom line, all of these rifles systems are excellent. There is no wrong choice. It's which do you like better, can afford, is available or is the deal. Not too many people are upset with owning any of the above listed options.