A mining proxy is similar to how you describe. Yes it allows you to have a bunch of miners appear as one miner to a pool, but just because you have a high amount of users being proxied to the pool, does not however mean:
doing almost all the mining job and sharing equally among all the users in the pool
Firstly, high user count does not necessarily mean high hashrate. It's very much hardware dependent. Secondly, there is no equal sharing. Miners get rewarded for the hashrate/difficulty of the jobs they submit - the more work you do, the higher percentage of any block rewards you get. Therefore your proxy only gets rewarded for the work it does (and thats the combined work of all your proxied miners).
Now onto pools.
users join to help mine faster unifying the power of all the pool.
is not really an accurate description of how pool mining works. A pool allows a group of miners to all agree that whoever in the pool mines a block, they will share the reward proportionally with all miners of the pool, based on how much work each miner does. The pool server just facilitates this and its operator takes a cut for running it.
Now, because a pool has many miners (thus higher hashrate), it will find blocks faster than any of the individual miners could find a block alone.
This brings us to one of the reasons miners use pools: to get regular payments. Total paid out over time will be roughly the same as if solo mined - the difference is frequent small payments vs infrequent large payments.
Another reason to join a 3rd party pool is ease. To mine to an existing pool, you literally just download and run a miner program pointed at the pool. True solo mining requires running a node.
Another reason is coin hopping. If you don't care which cryptocurrency you mine, many pools offer automatic switching to the most profitable coin at any given time.
So back to your core question:
Pool vs proxy for 1000 users?
Because a proxy is in effect, one pool miner, all payouts go to that one miner wallet. Therefore, how you intend to reimburse your users comes into play - how you (fairly) distribute the earnings. If one of your users has a lot of hashrate, surely they will want more rewards than a user with less hashrate. If all users have exactly the same hardware, this is less of an issue.
However, assuming your combined hashrate of all users is significant enough to get payouts at a frequency they are happy with, and you have the required experience to setup and run a pool, a private pool would make more sense. You are then not having to trust or rely on a 3rd party pool.
I'd suggest gaining more experience and understanding the subject matter better though. Start small and build your way up. It's one thing mining with your own time and hardware, but using your clients is another matter.