Simple, do both. Start with architecture, then do landscape. That's what I did.

Look at the licensing requirements where you are thinking of practicing - in many places an Architect may design landscapes in addition to buildings, but a Landscape Architect may only design landscapes.

 it completely depends on the scale that you want to work at.  If you end up doing residential, than it’s totally feasible to do both, and it would make more sense to pursue a degree in arch.  A garden is spatially rationalized in a way that’s not too different from a building, and you can learn to design gardens with the basic cognitive tools that you use to design architecture.  Large scale regional or urban landscape plans however will not cross over as much with architecture.  It’s truly a different beast.  

There are master programs that offer a joint M.Arch/MLA degree, they're often longer but if you want both then look into those. I was also in your position but eventually decided I'm more interested in MLA/designing public spaces so I went for that. Good luck! 

Look at programs that start with a combined foundation year- then select a ring in the circus to focus on.

Why choose. Do both.

As a building designer, I am kind of doing both building design and landscape design. For sake of conversation, I see the relationship as comparable to architecture & landscape architecture. Granted, landscape design work is currently few compared to building design projects. My point is supporting of what whistler said. At some point, you do pay attention to the title and words you use to describe services as there are states that regulates the title landscape architect and states that regulates both title and practice but I am not digging into that discussion for now for academic purposes, its good to learn both or at least take some courses in landscape architecture even if you are mainly in the field of designing buildings and you can likewise study in the inverse if landscape architecture is more in what you want to do but studying architecture courses can be helpful and useful for designing outbuildings and such. In the landscape design/landscape architecture realm, you may study courses in the horticultural subject matters and should as landscape design/landscape architecture services aren't just hardscape stuff after all and you will want to understand plants to make informed decisions.

Hi! I have recently found myself in the same boat. I applied to MArch 3 programs for this Fall 2022, and as I was researching programs I fell in love with landscape architecture. So on a last minute whim I committed to a school where I knew I could pick up a dual degree if I wish. I choose UVA which will take four years (w/o BArch), which is a long time but worth the extra year given the grand scheme of things. Most dual degrees would take the four years, unless you have a BA in Env Design or Arch already. In that case it's usually three.  

Some dual degree schools that have piqued my interest have been UVA, Wash U in St. Louis, Berkeley, Harvard, UT Austin (can accommodate an informal one), and I'm sure there are plenty more. Pratt just added a MLA and i believe they may have a dual degree option. 

Either way, I'm certainly excited to do both degrees and glad to see others interested too. Would be happy to connect more if you'd like! Good luck!