MattKing, is this because the scales are different - i.e., because Ilford papers require Ilford filters - or is it because the enlarger requires filters tailor-made for that enlarger?
I may pick up a "gel" type filter pack for use in the head, since the round plastic Ilford filters won't really fit in the lower filter drawer.
Generally speaking, it really won't matter which brand of filters you use. As long as you stay within the same set, you will generally achieve predictable results.
Some brands go slightly farther into the ends of the contrast range, but only with some papers.
In some cases, there have been multiple generations of filters. In Kodak's case, when they changed from Polycontrast papers to Polymax papers, they also brought out Polymax filters, and there were more in the box! The Polymax filters themselves do work with old Polycontrast papers, and vice versa.
The Beseler filters may very well have been manufactured by the same people as manufactured the Kodak, or Ilford (or Dupont?). The only advantage to Beseler filters may have been that they were sized to fit nicely into Beseler filter holders.
If the Ilford filters you have don't fall to the floor when you use them, and if their frames don't block the light, and if they aren't dirty or badly scratched, there is no great reason to replace them with the harder to handle "gel" filters.
By the way, the numbers on the filters themselves don't correspond to the contrast grades on fixed contrast papers.