I usually shoot with the cheapest color films available. In the beginning the main reason was that it was cheaper. I didn't really have a grasp of what slide film was and everything I was shooting was going to get developed at the local Walgreens. I was lucky to land quickly on Superia 400 and loved it's strong contrast and saturation, especially of greens and reds.
Conversely, professional color films promise a more realistic color rendition and less contrast so the photographer has a bit more control over the images. I found box of 5 rolls Fuji Pro 400H (expired 2013) in 120mm and jumped at the chance to try it out. To truly experience any emulsion I'd recommend trying it in 120mm. The larger format allows you to see the film on a larger scale that really tames any variation you may have from frame to frame on 35mm. 120 is going to make any strengths and issues with an emulsion apparent very quickly.
My approach with Fuji Pro 400H was to continue the same color and subject analysis as I had been doing with 35mm. I was shooting 400H with a Yeshica D TLR and a Hasseblad 500CM. I also added a roll of 220 (expired 2008) that provided very similar results as the fresher rolls.
Fuji color films always lean warm. 400H has the same characteristic saturation but it's much more subdued. While the reds and greens popped, they didn't take over the scene like they did with Superia. Blues and yellows weren't as fun but accurate and in control. Overall everything was accurate but flat.
The negatives that came back gave a much lower contrast profile that looked like I overexposed the images. I had to add contrast adjustment to most images I posted with 400H to get the typical look I preferred with Superia. It's interesting that Kodak's current color professional negative emulsion, Ektar, has strong contrast and warm profile that you'd expect from Fuji.
This leaves 400H in a weird spot. It falls into a no man's land for color emulsions. If you want the most accurate color emulsion you are going with Velvia while you can find it. If you want to shoot a negative film with more character you're better off with Ektar. If you want pleasing and accurate skin tones you go with Portra. If you want to save a few dollars you can try Lomography 400 which will give you accurate colors and a washed out look. That leaves 400H being the king of the color negative with a flatter contrast profile and slightly saturated greens and reds.
Color films should have a look that distances them from color digital where saturation and color are set on being as accurate, and boring, as possible. The emulsions that we associate with most with color film, Kodachrome, knew back then it wasn't accuracy that was king but enhancing what was already there. For me, Fuji Pro 400H doesn't do enough enhancement to stand out from it's peers.