Basically, you miss out a lot of sex scenes, and just get the existing scenes with Ian. It also depends on whether you allow Lena to have sex with Louise, Holly and Ivy, because apart from one scene with Ivy, the game doesn't seem to class those scenes as cheating.
The main difference though, is it forces Lena to do without Seymour's money. And his animosity towards her, means that she's blacklisted from virtually every modelling job in Baluart. So Lena really has to make money wherever she can.
If you open up their relationship though, then it presents the possibility of them having threesomes, depending on what Ian and Lena said were their sexual fantasies, during Ivy's birthday party. So far this has led to a threesome with Louise, if Ian and Lena said they both wanted a threesome with another woman. But if Lena fantasises about having sex with two guys, after that threesome she asks Ian if he'd be willing to do that for her, and Ian says he'll think about it. So I assume that's going to become an option down the line ( and I can't imagine it will be anybody but Jeremy). So with an open relationship, it increases the sex options, whilst remaining technically faithful.