My view is that all suspension designs have their good points and their bad points. Traditional straight axles provide a great look but are often associated with harsh ride and handling drawbacks due to each wheel transmitting its motion to the opposite wheel. A-arm independent suspensions are great for ride characteristics but their drawback is looks, particularly in older open wheel cars as the OP plans to build. Twin I-beams provide the advantage or independent suspension and traditional looks, but bring with them the challenge of camber changes and potential tire wear.
I don't doubt what Vince and adanteser are saying about their experience with the stock twin beam systems they have encountered. But in my experience there is a distinct advantage when using these axles in a hot rod vs workin on them in a stock F-150. And that advantage is the ability to design a chassis where you can easily control both caster AND camber.
In their stock configuration, caster and camber adjustments were a notorious nightmare for F-series owners. But in a properly designed hot rod, they are a snap.
By using a four bar system with adjustable radius rods, a simple twist of the rods will set your caster exactly where you want it. And with the use of air bags, coil overs, or adjustable quarter elliptical springs, you can also adjust camber quite easily. In fact, in my 32 pickup I can adjust the camber in 3-4 seconds by simply inflating or deflating my air bags. The coil overs on my roadster take 3-4 minutes to adjust camber. And with my quarter elliptical leaves, the process takes maybe 10-15 minutes.
Again, I would not argue that twin I-beams supply the perfect front suspension. I've build and run them all over the past 50 years...straight axles, mustang II, and twin beams. And I find the twin beams fit my personal needs and desires the best for the type of rods I build. But that all depends on what the owner/builder is after:
If you want a traditional look and are willing to sacrifice a bit of ride comfort - consider straight axle.
If you want great ride and you are running fenders - consider Mustang II or similar.
If you want a traditional look along with the comfort of independent suspension and you are willing to sacrifice a bit of tire wear - consider twin I beams.