For what it's worth, I used to be VERY against Savage rifles, just because of the constant references to poor finish, clunky operation, extraction/ejection problems, etc. And that's for both the rimfire and centerfire rifles. I couldn't understand why they had such a large aftermarket, or why anyone would be interested at all.
Over the course of about 10 years, I've had:
Savage Axis XP 22-250
Savage Axis XP 223
Savage Axis II 7.62x39
Savage 11 223
Savage 11 VT 308
And a bunch of different Mark II and 93 rimfires.
In summary, you could say that most are a hot mess of cobbled together parts that somehow punch WAY above their weight.
The Axis rifles all have several similar characteristics. The magazines don't always feed properly. They feel light and flimsy. They sometimes have ejection issues, which can be fixed by replacing the extractor ball bearing with one of 9/64" diameter. Works every time. AND they shoot incredibly well. My 223 gave me an all time personal best of a 1/2" 3 shot group at 200 yards with my handloads. Can't fault that. A friend with a Tikka Tactical 223 was constantly frustrated that my cheap, used 223 Axis would shoot group for group with his Tikka. I splurged for a $30 MCarbo trigger kit one day....even better.
The 11's are noticeably more substantial in feel, but almost identical design. The Axis is essentially a 11/110 'engineered' for cost savings. Both developed the extraction/ejection issue as above, and fixed just as easily. Both consistently shoot sub-3/4" three shot groups at 100 yards with handloads. Never had any feeding issues with either. The accutrigger is pretty good too, and a very simple design.
A couple other things to say in Savage's favor. Their customer service is very good. I've contacted them several times about issues with used rifles, and they have never balked at sending parts out. Another plus is that their bolt designs are standardized, so the extractor/ejector bits are identical (don't quote me on that, but I think so) and a kit for one will work on the other rifles. Finally, they have to be the most productive manufacturer ever. It seems only during the biggest sales that any model or chambering isn't available and even then it's temporary. It's common to get either Axis or 11/110s on a very reasonable sale price.
In the end, it depends what you're looking for. If you need ooohs and aaaahs at the range when you open your rifle case, they may not be for you. If you like ooohs and aaaahs when you check your targets, and don't want to spend too much, maybe they are.