Depends on a lot of factors--the neighborhood class, your target tenant, and nearby availability.
If the majority of the complexes around you have updated in, say, the last 10 years, and your stuff was last updated 15-20 years ago, you can probably get by, but you may have to charge a rent slightly below market.
If you're in an A-class neighborhood, everything around you will be pretty up-to-date. If your stuff is 5-10 years behind, again, you'll probably have to charge a rent slightly below market and will likely attract mid-upper B-class tenants. This could actually work out very well in your favor.
Of course, if everything around you has been updated in the last 5-10 years and you're 25-30 years behind, you definitely need an upgrade.
You can't rent a slum, so I would say that the units need to be in overall good shape and clean. As far as being modern or not... you may have a dated unit in great shape which a "good tenant" will respect. You may not get the premium rent if it is not modern though. If the unit is completely blown out, I would tend to think a more desperate applicant would be interested. A respectable tenant would want a respectable landlord who maintains the property. Dated is okay. Deferred is not. Hope this helps to shed some light.