I’m on a full frame so your milage may vary. . . I’ve had the 28-135 f/3.5-5.6 IS and the 24-105 f/4 L. The 24-105 is a much better lens, and in my opinion worth every extra cent I paid for it over the 28-135.
It might hurt the wallet up front, but it’s usually better to pay once than to be constantly upgrading. However, if you have a cropped sensor you may wish to go wider.
For landscape photography, I use a lot of manual focus Nikon Lenses from the ’70s and ’80s on an adaptor. The image quality is usually fantastic and these lenses can often be had for very little $$$. However, these aren’t really walk-around lenses I only mention them since you mentioned you’re interested in landscape photography and on a tight budget.