Compass, a lot of this advice is a shot in the dark without more information about your 450.
It could have a Dana 80, it could have a Dana 110. It could have a 7.3, a 6.0, or a 6.4. It could have a 4R100 or a 5R110W. The axle, engine, and transmission could be material factors in the decision and in the recommendations people make.
If you posted your model year, and any other information you know about your F450, it might bring you more specific recommendations.
Speaking as someone with 4.88's also, in an F-550, here are some observations I've made over the last dozen or so years with this combination:
TIRES:
Upgrading to larger tires to make the final drive taller is a bit more difficult and expensive to do "right" than it is for 16" tires, as a previous poster suggested.
The next size up for the 19.5 is a 245/70R19.5 (up from the factory 225). The problem with mounting 245's is that the stock F-450 wheels are not wide enough to meet the minimum rim width specification for 245s. Our OEM wheels (both steel and aluminum versions) are only 6" wide, and a 245 requires 6.75" minimum, with 7" being preferred for proper tire shoulder support when cornering.
New wheels are very expensive, and used wheels, or take offs, are almost impossible to find, especially if the F450 is older than 2005, where an 8x225mm bolt pattern is used instead of the current 10x225 bolt pattern. Since NO F450 pickup or chassis cab came with 6.75" wheels, one most turn to the F53 stripped motorhome chassis (of only certain GVWRS... as not all had the same wheels) to try and find wide enough wheels with the additional offset to maintain dually tire spacing.
So while all this is doable, it will not be without considerable effort or expense. Probably both. To reshoe a 7 wheel set of 19.5 tires will run about $2,500 for good rubber and an unknown amount for the wheels.
AXLES
Lot's of F450 chassis cabs came with the Dana 80 rear axle, which might be a little less expensive to regear than a Dana 110. If you have the F450 pickup from 2008-10, then you likely have the Dana 110.
TRANSMISSIONS
When comparing rear gear ratio's, lots of folks just look at the final drive ratio of the transmission... which is typically around .71 more or less in overdrive. But poster CarringB makes an excellent point to consider the intermediate gear shift points, especially in an automatic transmission where the driver does not always choose every single gear. Too tall of a final axle ratio can turn a 4 speed transmission into a 3 usable speed transmission when towing, but even harder to determine without study is the amount of leg each trans gear will have with a given rear gear ratio. This is a really good point by carringB, and should be well considered before making any change.
Sometimes, fuel economy goes DOWN with a change to a taller axle gear, due to reduced economy when climbing in lower transmission gears when the next gear up now lugs with the new axle ratio.
ENGINE
If your truck has a 6.4L or 6.0L diesel engine, some consideration should be given to the value and expected life of the truck before costly engine and fuel system repairs (to the tune of 5 figures) might need to be made to keep the truck on the road. You mentioned considering either a gear change or a new truck.... and depending on the engine in your current truck, you might be dollars ahead changing trucks.
On the other hand, if your current truck has the V10 gas engine or the 7.3L diesel engine, then you will likely be many dollars ahead by keeping your current truck and going ahead with fixing it to your liking.
SPEED
That's what it I determined it boiled down to in my case. If I kept the 4.88's and kept my speed at or below 55 mph, then I could keep my money in the bank rather than throw it at the rear end of the truck.
There just isn't enough benefit going 65 mph to justify the expense in a gear change. I can accomplish the same economy by keeping my speed in check, which keeps the noise level down too.
