I'm having a very good experience with 8.1 on my Lumia 625. A lot of the bugs and gripes other people have mentioned, I've mercifully not had. There's been a lot of hate for Xbox Music, but I always used Nokia MixRadio anyway. I've had to set my phone region and language to US (I'm in the UK) to be able to use Cortana, but that works great--no problems with the store. I haven't noticed too much of a battery drain, and I haven't experienced any lag. The calendar app was not missing as some have said. I only ever have 1 or 2 games installed, so I'm not at all outraged by having the games showing up in the main apps list, though I can see what some people would hate that. There are one or two little niggles which I have, which are just that--niggles.
1) Cortana gives me temperature in Celsius instead of Fahrenheit, unless I specifically ask for it, but she doesn't know I'm British and would prefer not to subtract 32, multiply by 5, then divide by 9 every time I want to know what the temperature is. So, I can forgive her for this. She also only gives me US news, obviously for the same reason. However, it would be nice to be able to choose from several news sources here.
2) The photos hub is much less pretty than it used to be. It was gorgeous in 8.0. It's really rather bland and uninspiring in 8.1.
3) The fact that facebook integration has been moved to a separate app, and the whole sharing system is different. Sharing links doesn't work quite right, and I haven't yet been able to share to Twitter. (To be fair, I've only tried to share from Nextgen Reader, so it wasn't a comprehensive test.)
4) I wish we could have more than four toggles in the action center. I think at least 5.
5) I miss the agenda view in the stock calendar, and I think the redesign here is really not Microsoft's best aesthetic work. However, I use Cal anyway, so this is no biggie for me.
6) Unless there's a setting I haven't found, the action center doesn't group notifications from the same app, i.e. instead of giving me one notification saying I have 12 emails, it shows me all 12 emails in a long list. This is faster I suppose, and from a certain point of view, more efficient, but it's also messy.
Overall, however, I have to say I love the update.My niggles are all things I can live with, either in the long term, or until an update comes along to improve things. I was able to uninstall a handful of apps I had before because the OS now does the job that they did for me by default. The action center, tile backgrounds, the word flow keyboard are great, and the store redesign is excellent. I think the addition of Maps for non-Lumia phones which don't have Here Maps is also great, (though testing one against the other I have to say Here Maps consistently found me quicker routes.) I like that certain things have been added to the apps list, i.e. storage sense, battery saver, etc, as it makes it quicker to access these things. I understand that a lot of people are incredibly incensed by 8.1, and if they're the people experiencing bugs and lags I can understand why, but I really don't share that view.