"...Are Enfields in .308 very common?..." Not really. They're out there, but not nearly as many as the standard .303's.
A lot depends on who did the conversion. DCRA No. 4 rifles, if you can find one, were done properly. So were the Brit Enforcer's and L39A1/L42A1. They look like sporters(target sighted or scoped), but were converted by the Brits for use as sniper rifles. India built a bunch that look like a No. 1 Mk III(Ishapore 2A1. Squared mag), from new materials, in the 60's and there are some that are just rebarreled without changing the mag.
"...the AIA rifles..." Pricey and a lot of rumours about the quality.
"...a CAI converted..." Century assembled thousands of Lee-Enfield rifles out of parts bins with zero QC. Not even checking the headspace to ensure the rifles were/are safe to shoot. While you should always check the headspace on any Lee-Enfield, it's especially necessary on any rifle Century had anything to do with.