Argthtjtr

The word "alternative" would work here. It's pretty versatile, so it should cover your context. It can be used no matter the level of formality you want and can be used to describe a wide variety of things. Here are some examples:

• 
  

  We present two quicksort alternatives for cache optimizations which work well on both balanced and unbalanced data sets.
  _{Improving Memory Performance of Sorting
  Algorithms}

  
  




• 
  

  Is ReactOS a viable Windows alternative? Taking the OS for a test drive

  
  




• 
  

  The preferred alternative to this method is orElseThrow().
  _{OptionalLong (Java SE 11 & JDK 11) - Oracle Docs}

  
  




• 
  

  Our selection actually contains more than 20 libraries, as some of them are alternatives to each other and solve the same problem.
  _{Top 20 Python libraries for data science in 2018}

  
  

I would say that method1 is method2's equivalent:

A person or thing that is equal to or corresponds with another in value, amount, function, meaning, etc.

https://en.oxforddictionaries.com/definition/equivalent

The term "functionally equivalent" springs to mind.

e.g.
The methods are functionally equivalent.
or
A Functional equivalence exists between method1 and method2.

It seems to me that what is salient isn't a property of a method (viz that it can solve a task that another method can solve), but rather a property of a task (that there are two methods that solve it). There's the phrase "there's more than one way to skin a cat".

There's more than one way to skin a cat.

I think this is more appropriate as it more explicitly relates to processes for achieving something instead of a more abstract comparison.

Definition:

There are many methods one may employ in achieving one's ends.

Used like so:

We can go with method A if you like but there is more than one way to skin a cat.

All roads lead to Rome:

As a proverb, it refers to the fact that many routes can lead to a given result.

Another metaphorical idiom would be "That's six of one, half a dozen of the other" — i.e. it doesn't matter which, they are equivalent.

This idiom cannot be used to describe one method in relation to the other; I like the modification of the cat skinning metaphor suggested by JonM for that: "Method B is just another way to skin this cat", or similar.

If both methods for solving the problem are equally good, regarding the choice between them you could say:

It's as broad as it's long.

Macmillan says this expression is

used for saying that you cannot choose between two things or actions because they are equal

Macmillan also words the phrase slightly differently than I know it: It's as broad as it is long. It also lists the phrase as British and spoken.

The spoken is important. This phrase is definitely conversational and not technical: you wouldn't write it in a paper. Hence, this is really only an answer to your first question: [Are] there any terms/phrases or succinct ways to describe such pairs of methods?

I always took it's as broad as it's long to suggest a piece of wood that could be sat on either side: it wouldn't matter which, as it is square. That may well not be its actual origin, but it does express the equilateral geometry of the metaphor of the phrase.

With it's as broad as it's long, the essence is that it would make absolutely no difference if you went about solving the problem one way or the other, but the choice must between two equivalent options. (You could try it's as broad as it's long as it's high for three interchangeable alternatives, but at that point you've gone off piste and you're on your own.)

(Personally, I think the idea of exact equivalence might be more elegantly expressed by: it's as broad as it's wide. However, I couldn't recommend that as an option!)

Such methods are two sides of the same coin:

Definition
To be two things that seem disparate but are actually related.

Usage instance:

"He gave me two methods for solving a problem, which are two sides of the same coin."

I would call the two methods coequal.

Definition
Equal with another or each other in rank, ability, extent, etc.

Usage example:

Methods 1 and 2 are coequal in their ability to handle the task.