Blitz 10 minutes vs 3


the obvious answer would be that 10 minutes Blitz is definitely deeper just like you can't compare 1 minute to 3 minutes. do you agree?

I have some experience in both time controls, but my favorite time control (by far) is 10 minutes.
Your question is interesting, but I think it is hard to compare chess abilities between ANY time controls. Some are simply strong at fast paced chess and some at classical chess (long games, similar to daily on chess.com). For the most part though, faster chess (like bullet/blitz) are merely reflections of ones true chess ability. If someone is rated OTB 2000, Id' expect at least 1700 or so blitz play. Some are simply bad under certain time controls, but the ratings should be within a few hundred points or so, regardless. A player's rating only indicates approximate level under those controls - which is why chess.com ratings are separated (bullet/blitz/daily etc.)
Personally, I prefer "slower" chess like OTB classical chess. However, I do not want to wait at a computer screen for too long (my schedule is a bit busy). I especially do not want to wait indefinitely for someone who won't move/connection issues/vacation time etc. I would play daily more often, but I feel that chess loses something if not free flowing. Daily chess is still helpful, but I feel like they are closer to puzzles than actual games. I naturally move somewhat quickly, but I also desire plenty of "extra" time to calculate deeper lines, or convert a delicate endgame. 10 minutes (after a little experimenting) feels natural for me. I may choose longer, but opponents letting the clock run out when lost, and connection waits, makes me choose a somewhat shorter time - at worst a ten minute wait is okay for me. As a result, my favorite on chess.com is 10 minute blitz (of course I still play a lot of longer games OTB); however, I do not know if you can really "compare" my blitz rating to other time controls too well. I expect a few hundred points of deviation among really ANY time controls - but fairly accurately, I do not think your forum question is answerable. It is a cool thought, but I think that the accurate rating would deviate too much to be beneficial.