I don't know which of the EF-S 18-135s you've got... the older, orignal micro motor version... the faster/quieter focusing STM version.... or the latest and greatest and even faster focusing Nano USM version (Canon claims 2X to 4X faster than the STM). But the last two have the same optical formula, improved over the first.

The EF-S 18-200mm has IS, but is a micro motor lens. I wouldn't expect it to have near the AF performance that the STM or USM version of the 18-135mm both offer... if you have one of those.

Compare for yourself at https://www.the-digital-picture.com/Reviews/ISO-12233-Sample-Crops.aspx?Lens=1045&Camera=963&Sample=0&FLI=5&API=1&LensComp=476&CameraComp=963&SampleComp=0&FLIComp=4&APIComp=1, but to me it appears that the newer 18-135s offer better IQ.... sharper in the corners especially, less chromatic aberration... at every focal length they share.

Besides, the difference between 135mm and 200mm is approx. 4 or 5 steps forward.

A pretty good lens for its type, in its day (2008)... Maybe it was even one of the best "do-it-alls" ten years ago when Bryan Carnathan reviewed it for The-Digital-Picture.com way back then. But the EF-S 18-200mm now doesn't appear to be as good IQ as some similar, but more recent lenses of that type from other manufacturers. For example, Carnathan is a lot less enthusiastic about the Sigma 18-200mm from 2014, even though to my eye it appears to have the edge in image sharpness over the Canon at most focal lengths: https://www.the-digital-picture.com/Reviews/ISO-12233-Sample-Crops.aspx?Lens=946&Camera=736&Sample=0&FLI=5&API=1&LensComp=476&CameraComp=736&SampleComp=0&FLIComp=4&APIComp=1 The Sigma also has HSM ultrasonic focus drive, which I imagine can run circles around the micro motor in the Canon.

Still, I'm just not a fan of 10X (and greater) "do-it-all" zooms.... They always have to compromise in some ways and sort of defeat the whole purpose of getting an interchangeable lens camera in the first place. Granted, ultra wide ranging zooms may be convenient... might even be important or necessary for some things like travel where gear is very limited.

And in this case I'll never know. Because much of what I shoot is sports and wildlife, I generally avoid slower focusing micro motor. I own two (one is a macro lens, where it slower focus is typical regardless... the other is an ultrawide, where so little movement of the focus group is needed, any delay is imperceptible). Everything else... particularly the lenses I use most for action photography, are USM.

Besides, with an 18-135 you are within a few steps of 200mm anyway.... And if your 18-135 is one of the two newer versions, you've already got a sharper, better corrected, versatile walk-around lens.

EDIT: I was really surprised to see they're asking $700 for the EF-S 18-200 new (plus it appears to lose half its value used, a lot more depreciation than most Canon lenses while still in production)!

Heck, for that kind of money... or even less... I can think of a number of other lenses I'd buy instead! Telephotos would include the new EF 70-300 IS Nano USM II, for example, now going for $500. The EF 70-200mm f/4L USM (non-IS version) is currently on sale for $600. The EF 200mm f/2.8L USM II is $750. None of those would be light and convenient as a "do it all" 10X zoom, but they all offer a lot of other advantages.

Now, if you've just got a case of G.A.S..... If it were me I'd pick up an EF-S 10-18mm IS STM to stick in a pocket and take with me. Under $300 and it would extend your focal length range into new territory, rather than just duplicating focal lengths you've already got.

I'm thinking maybe the 100-400 is a bit large and heavy for 'good walk around'. The Digital Picture's review of the 18-200 is very positive and reads like a worthy consideration for a crop body giving a zoom between 18mm wide and 200mm long. If 18-135 isn't versatile enough, the 18-200 seems like the next valid option. But, the idea can be expressed as $700 to buy another 65mm and what becomes of your 18-135?

When you're out and about, are you all over the zoom range or always zoomed to the long end, say 50mm and up? If zoomed, that would put you back in the 70-200 / 300 market where size and weight come back into the discussion, particularly for IS-enabled lenses.

Since the question was about the 100-400L II and the 1.4x, here's a variety of images (close and far) that show the detailed captures this configuration can capture with a camera that supports AF at f/8. They're presented large so you can easily see the details ... If you're curious about the focal length and aperture, click the URL where the details for every image is available. If too larger for your screen, they'll resize to your local display if you click the URL title for each image.