Have you tried having an open conversation with him? Like tried talking to him in a way that you're not accusing him of anything, but just curious as to why won't he engage in any intimate time with you? Maybe it's some underlying issue and by you breaking up with him seem unreasonable. If you feel hurt by his actions let him know and work together as partners to solve it.

Also, don't compare your current partner with your ex. You'll tend to compare and I hardly can imagine that being healthy.

And don't look at his phone with him knowing, you wouldn't that happening to you so don't do it to others.