I've not seen a consensus on this matter, ever, (and I probably never will) so it really comes down to what each installer feels comfortable with, whether or not they do the job themselves - or sub it out (the only person who tiled
last was one who wanted to make sure the cabinets guys didn't mess up his floor, so he always tiled last). So, this ain't no 'NO BRAINER...'
More often than not, DIYers have the same intentions as pros do in matters such as this; I mean, they both want the best 'look' possible, they want the most ease of use, perhaps lowest maintenance, they want it done as efficiently as possible and at the lowest overall cost. Here, there are certain problems I'd be more concerned with than saving a few bucks on tiles under a cabinets...put another way, "saving money" has never dictated the way to go over "proper install". And the reason is that the pro usually has a better grip on a long term vision, whereas the DIYer only see his/her own situation. For example, there are certain plumbing fixtures we recommend, because they have a better track record for repairs. More expensive yes, but
worth it in the long run. A DIYer might think that saving $35 on a cheaper faucet is $35 in his pocket - until a year later he has to fork out $150 to have someone come in and replace it...
That's why IMO it is better in the long run to tile first and forget about saving a few bucks. You'll probably pay that back in the end.
We like to put tiles down
in relation to the cabinets... not "just up to the wall" as we don't like cabinets sitting on grout lines. It has to look good
and be done (what we think is) "right". So watch it for 12 inch tiles under 24" cabinet bases...
At the same time, ironing out upper cabinet height problems is easy for us, as compared to tiling problems. Plus, we like to let people know all the pitfalls of the way we do things after we leave. I don't want a call-back in three years time asking us why we didn't tell them that our job makes remodelling of their kitchen impossible because the appliances are stuck in...
So, sure you'll get pro and DIY opinions on this - and everything. There's no "right" way, I guess, just the most-used way amongst people who do this for a living.
One thing I would address long before we debate over the tile situation is whether or not your floor is suitable for tiling - a matter no-one has thought to address with this poster...I'd spend my time there first